3A95.50  Chaotic Pendulum

PURPOSE: To show chaotic motion.

DESCRIPTION: A double pendulum is a device that consists of two physical pendulums linked together.  It appears to be a simple mechanical system, a variation of the physical pendulum.  One might expect the motion to be  predictable in some way.  And for a small initial displacement from equilibrium, as shown in the photo at left, the motion is indeed predictable and deterministic. 

But if it is forced to have a large initial displacement from equilibrium, as shown in the photo at right, the nature of the motion changes dramatically into chaotic motion.  The motion does not repeat.  It is fun to watch.  The chaotic treatment is needed to describe the behavior.

Some students consider this to be a favorite demonstration. 

EQUIPMENT:  Chaotic pendulum, as photographed.

DEMONSTRATION VIDEOS:(in real time)

(in slow motion; NOTE: If you are using Internet Explorer, please be patient as this takes a couple of minutes to load.)

SETUP NOTES: This demo is constructed from the plans published in Am. J. Phys., Vol. 60, No. 6, June 1992 Pages 491 - 499

For more about this chaos demo and others:

W. Stadler, Am. J. Phys 50, 595-598 (1982).

 

Stephen F. Felszeghy, On the adequacy of Newtonian particle mechanics for solving the rigid double pendulum problem, AJP 53, 230-232 (1985).

 

W. Stadler, Rebuttal to "On the adequacy of Newtonian particle mechanics for solving the rigid double pendulum problem," [AJP 53, 230-232 (1985)], AJP 53, 233-234 (1985).

 

Shinbrot, Grebogi, Wisdom, and Yorke, Chaos in a Double Pendulum, AJP 60, 491-499, (1992).

Supplemental Information Sheet, T. Shinbrot, (1989).

 

R. B. Levien and S. M. Tan, Double pendulum: An experiment in chaos, AJP 61, 1038-1044 (1993).

 

Richard V. Mancuso and Elise M. Somerset, Changing of the State of a Diode and Chaos, TPT 35, 31-33, (1997)

 

Azad Siahmakoun, Valentina A. French, and Jeffrey Patterson, Nonlinear dynamics of a sinusoidally driven pendulum in a repulsive magnetic field, APJ 65, 393-400, (1997)